Using a shirt to dry clean hands might not be a bad option.
The laundering of cloth towels brings its own environmental load. I don't know that that load may be, but some studies have indicated that the environmental load of cloth diapers is greater than that of disposable diapers, so I wouldn't be shocked to learn that the environmental load of cloth towels were greater than that of paper towels.
(Hands could be air-dried, but would then tend to chap.)